Subtracting Fractions

, (that is understanding what is the UNIT of the group of elements we are working with) is well understood. And the concept of partitioning goes along with it.

The unit is defined by the denominator (the bottom number).

The rules goes that

you cannot subtract fractions with different denominators!

(
or, conversely, you can subtract fractions which have the same denominator only!

)

One common mistake first algebra learners have is to mistakenly subtract two fractions which have no common unit (or denominator) in this way:

1/6 - 1/2 = 1/4 (wrong !)

or

subtracting numerator and denominator as in a normal subtraction, like this:

8/5 - 2/3 = 6/3 (wrong !)

Instead, you must "do your maths"::

4/3 - 1/3 = 3/3 = 1 (correct!)

So, when subtracting fractions, mind the bottom numbers (the denominators)!

Are they the same? If positive just subtract the top numbers together and leave the bottom numbers as you found them!

603. The examples which a beginner should choose for prac-
tice should be simple and should not contain very large num-
bers. The powers of the mind cannot be directed to two things
at once; if the complexity of the numbers used requires all the
student's attention, he cannot observe the principle of the rule
which he is following. DE MORGAN, A.

601. The first thing to be attended to in reading any algebraic
treatise is the gaining a perfect understanding of the different
processes there exhibited, and of their connection with one an-
other. This cannot be attained by the mere reading of the book,
however great the attention which may be given. It is impos-
sible in a mathematical work to fill up every process in the man-
ner in which it must be filled up in the mind of the student before
he can be said to have completely mastered it. Many results
must be given of which the details are suppressed, such are the
additions, multiplications, extractions of square roots, etc., with
which the investigations abound. These must not be taken on
trust by the student, but must be worked out by his own pen,
which must never be out of his own hand while engaged in any
mathematical process. DE MORGAN, A.